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A193558 Differences between consecutive primes of the form k^2+1. 6
3, 12, 20, 64, 96, 60, 144, 176, 100, 620, 304, 1316, 220, 1220, 1120, 1580, 1044, 736, 3264, 1356, 944, 976, 500, 1024, 1056, 3360, 1184, 1836, 1264, 3300, 2076, 1424, 1456, 7760, 820, 1664, 6076, 2724, 2796, 1904, 4900, 3036, 2064, 2096, 3204, 5500, 2256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that the sequence of primes of the form k^2+1 is infinite, but this has never been proved. This sequence contains a subset of squares: {64, 144, 100, 1024, 4900, 10816, 11664, 12544, 18496, 102400, 41616, ...}.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2) = 12 because (4^2+1)-(2^2+1) = 17 - 5 = 12.

MATHEMATICA

Differences[Select[Range[250]^2 + 1, PrimeQ]]

PROG

(PARI) lista(nn) = my(v=select(x->issquare(x-1), primes(nn))); vector(#v-1, k, v[k+1] - v[k]) \\ Michel Marcus, Dec 04 2020

CROSSREFS

Cf. A002496.

Sequence in context: A122576 A212760 A143268 * A256131 A080767 A043465

Adjacent sequences: A193555 A193556 A193557 * A193559 A193560 A193561

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jul 30 2011

STATUS

approved

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Last modified December 2 07:55 EST 2022. Contains 358493 sequences. (Running on oeis4.)